Bulletin of the
Korean Mathematical Society BKMS

Let $\Omega$ be a bounded Lipschitz domain in $R^n$, $5\le n \le 7$. We will show that the solution $u\in W^{2,2}_0(\Omega)$ of the equation $\Delta\Delta u=f \in L^{\infty}(\Omega)\quad\text{ in }\Omega$ is H\"older continuous up to the boundary of $\Omega$, that is, $u\in C^{0,\alpha}(\overline{\Omega}), \alpha>0$.

Keywords: Biharmonic equation, regularity, Lipschitz domain

MSC numbers: 35B65, 35C15